Theorem cnvimass

Description: A preimage under any class is included in the domain of the class. (Contributed by FL, 29-Jan-2007)

	Ref	Expression
Assertion	cnvimass	$$⊢A^{-1}\left[B\right]\subseteq \mathrm{dom}A$$

Proof

Step	Hyp	Ref	Expression
1		imassrn	$$⊢A^{-1}\left[B\right]\subseteq \mathrm{ran}{A}^{-1}$$
2		dfdm4	$$⊢\mathrm{dom}A=\mathrm{ran}{A}^{-1}$$
3	1 2	sseqtrri	$$⊢A^{-1}\left[B\right]\subseteq \mathrm{dom}A$$